Considering that TPE [1]} used tree structure to model the sampling of hyperparameter settings, we propose to employ a binary tree to build the hierarchical search space, as shown in Fig. REF . Each pathway from the root node to a leaf node represents a subspace of the whole hyperparameter space. For example, from root to node \(c_{0}\) , the child nodes (\(s_{0}, l_{0}, f_{0}, n_{0}\) ) define the corresponding ranges of hyperparameters (batch size, learning rate, the size of graph convolution layer, and the size of fully-connected layer), which forms a subspace of the whole search space and can be represented by a binary string 0000. Meanwhile, the left and right child nodes define the lower and higher ranges of hyperparameters by thresholds. For example, if \(s\)  ranges from 8 to 512, the median value 256 is chosen as the threshold to give two subspace with the same size. \(s_{0}\)  indicate a range from 8 to 255 and \(s_{1}\)  ranges from 256 to 512. In this way, the whole search space is divided into many subspaces, and the number of subspaces equals the total number of leaf nodes \(c\)  (i.e., the maximum width \({n_{s}}\) ), or the square of the dimension of hyperparameter settings \({n_{h}}^{2}\) , where \(n_{h}\)  is also the maximum depth of the tree without leaf nodes.
